15. Express as a polynomial in n.
 
16. Express compactly without using the  notation.
 
17. Show that 

18. Show that 

19. Evaluate  and show that they are not always equal.

20. Show that 

21. Prove by mathematical induction that 

22. Prove that 
 
23. Express  as a polynomial in n.

24. Express  as a polynomial in n.

25. Write  as a polynomial in n, and then use the fact that 
is always an integer to give a new proof that n(n² + 5) is an integral multiple of 6 for all integers n.

26. (a) Write  as a polynomial in n.
 
(b) Show that n⁴ - 2n³ + 11n² + 14n is an integral multiple of 24 for all integers n.
 
 

Monday, June 8, 1998